Why do you need to use special right triangles ?

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Solution

Use of special right triangle.
Special right triangles help to quickly calculate various length in geometric problems.
Angle-based right triangle of $30 ° - 60 ° - 90 °$ is type of special right triangle used for rapidly reproducing the values of trigonometric functions.
$45 ° - 45 ° - 90 °$ right triangle makes an isosceles right triangle and has the smallest ratio of the hypotenuse to the sum of the lengths of other two sides, $\frac{\sqrt{2}}{2}$ .
Angles of right triangle $30 ° - 60 ° - 90 °$ have angles in the ratio $1 ˸ 2 ˸ 3$ so, they are in arithmetic progression.
Hence, there is need of special right triangles to make the calculation easier or to form simple relationship while solving various problems.

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